The Geometric Sequence | Calculating the Sum of the First Eight Terms

Find sum of the first eight terms of the geometric series; 3+6+12+…

To find the sum of the first eight terms of a geometric series, we need to determine the common ratio (r) and use the formula for the sum of a geometric series

To find the sum of the first eight terms of a geometric series, we need to determine the common ratio (r) and use the formula for the sum of a geometric series.

In the given series, notice that each term is obtained by multiplying the previous term by 2. This shows that the common ratio is 2.

Now, let us use the formula for the sum of a geometric series:

Sn = a * (r^n – 1) / (r – 1)

where Sn is the sum of the first n terms, a is the first term, and r is the common ratio.

In this case, the first term, a, is 3 and the common ratio, r, is 2.

Plugging these values into the formula, we get:

S8 = 3 * (2^8 – 1) / (2 – 1)

Simplifying:

S8 = 3 * (256 – 1) / 1

S8 = 3 * 255

S8 = 765

Therefore, the sum of the first eight terms of the geometric series 3 + 6 + 12 + … is 765.

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